The VIRCATOR comprises a diode constituted by a cathode 2 and by an anode 3+4, emitting a beam of electrons 1, as well as by a cylindrical wave guide 5. The anode is constituted by a thick frame 3 and by a thin sheet 4 (frequently called “thin anode 4” below by simplification). By “thin” it is meant here that the sheet of the anode 4 has a thickness of the order of the micrometer, that is to say of a few micrometers or even of a few tenths of micrometers. The thin sheet 4 is coupled to the cylindrical wave guide 5. In other words, the thin anode 4 separates the cathode 2 from the cylindrical wave guide 5 by being situated at an entrance to the wave guide 5, at an interface between the thick frame 3 and the wave guide 5; and the thick frame 3 generally surrounds the cathode 2.
This type of device is known to produce high power pulses of microwaves
To that end, a potential difference is applied to the terminals of the diode 2+3+4 creating an electronic emission at the location of the cathode 2. When the density of electron current emitted exceeds the Child-Langmuir current density limit, the electron beam 1 disintegrates under the effect of its own space charge. At the location of the thin sheet 4 of the anode, the components of the electric field that are transverse relative to an axis z representing a longitudinal axis of the wave guide 5, cancel out. The electron beam 1 then begins to be pinched under the effect of its magnetic field. When the current entering the cylindrical wave guide 5 exceeds the space-charge current limit (referred to as “critical” current, denoted Ic), the electron density becomes so great that the beam can no longer propagate within the wave guide 5. An accumulation of charge 6, commonly called “virtual cathode 6”, then forms beyond the thin sheet 4. The virtual cathode 6 then deviates numerous electrons to the extent of sending some back towards the cathode 2, through the thin sheet 4.
In a relativistic regime, an estimate of the critical current Ic is given by
      I    c    =                    4        ⁢                                  ⁢                  πɛ          0                ⁢                  mc          3                    q        ⁢                            (                                    γ                              2                /                3                                      -            1                    )                          3          /          2                            1        +                  2          ⁢                                          ⁢                      ln            ⁡                          (                                                R                  G                                r                            )                                          
With γ=1+qV/mc2, where q is the charge of an electron, V the potential difference applied between the electrodes of the diode 2+3+4, m is the mass of an electron at rest, c is the speed of light and ε0 is the permittivity of a vacuum.
Considering the disintegration of the beam on emission in the diode, the radius of the beam r entering the wave guide is of the order of the radius of the cylindrical wave guide RG. An order of magnitude of the critical current Ic (in kilo-Ampere) is then given by the following simplified expression:Ic≈17(γ2/3−1)3/2 
While approaching the thin anode 4, the virtual cathode 6 increases its charge density until the time at which it disintegrates under the effect of its own space charge and a new virtual cathode rebuilds a little further away in the wave guide 5. This is the oscillation principle of the virtual cathode which is at the origin of an emission of a microwave wave 7.
FIG. 1 represents a formation of a virtual cathode oscillator in a VIRCATOR type device of the prior art when the current of the beam exceeds the critical current in the wave guide 5. FIG. 2 represents the characteristic signature, referred to as “diamond-shaped” of the virtual cathode oscillator 6 in the phase space with the acceleration and the deceleration of the electrons on passing the thin anode 4 on their path from the cathode 2 towards the virtual cathode 6 and vice-versa, that is to say the quantity of motion in the longitudinal direction and as a function of the longitudinal position.
The virtual cathode 6 moves around an average position which is situated at a distance from the thin anode 4 approximately equal to that separating the thin anode 4 from the emitter cathode (the latter distance being designated by dAk). The electrons which are sent back by the virtual cathode 6 towards the cathode 2 passing through the thin anode 4 are modulated to the frequency of the microwave wave 7 and interact with the electron beam 1 created in the space between the cathode 2 and the thin anode 4 while modulating it slightly. These backscattered electrons are braked between the thin anode 4 and the cathode 2. They are also mainly deviated towards the frame of the anode 3.
In parallel, the electrons which cross the virtual cathode 6 take back energy from the microwave wave 7 which propagates in the wave guide, so reducing its intensity.
The dimensioning of an axial VIRCATOR according to the known state of the art is the following:
The frequency f of the emitted wave 7 (expressed in GHz) is a function of the distance dAk (expressed in cm) that separates the cathode 2 from the thin anode 4, and of the relativistic factor γ of the electrons at the location of the thin anode 4 in relation with the potential difference applied to the diode 2+3+4. This frequency may be estimated by the following formula:
  f  =                    4        ,        77                    d        Ak              ⁢          log      ⁡              (                  γ          +                                                    γ                2                            -              1                                      )            
The microwave wave 7, having axial rotational symmetry, progresses in modes referred to as “transverse magnetic”, designated by “TM0n”, the axial component of its magnetic field being nil. In order for it to propagate inside the cylindrical guide 5 only in mode TM01, the radius RG of the cylindrical wave guide 5 must be greater than the cut-off wavelength of the following mode TM02. The equation below (and not the inverse formula which turned out to be erroneous) takes account of these propagation conditions:
                    k        01            ⁢      c              2      ⁢                          ⁢      π      ⁢                          ⁢      f        ≤      R    G    ≤                    k        02            ⁢      c              2      ⁢                          ⁢      π      ⁢                          ⁢      f      where k0n represents the root of the equation of the Bessel function J0(k0n)=0, with k01=2,4048 and k02=5,5201.
The length of the wave guide 5 is, preferably, equal to several times the wavelength λ of the electromagnetic wave 7 (λ=c/f).
The best operation for coupling the virtual cathode 6 with the electromagnetic wave 7 is obtained when the maximum density of the virtual cathode 6 at its average position is situated in the neighborhood of the maximum of the radial component of the electric field of the electromagnetic wave. Considering that the electromagnetic wave 7 propagates in the TM01 mode alone and considering also the disintegration of the beam on emission, the radius Rc of the cathode 2 then, preferably, verifies the following relationship:
      R    c    <      1    ,    8412    ⁢                  R        G                    k        01              ≈      0    ,    75    ×          R      G      
The device described above is of simple design. Its operation is robust and does not require recourse to an external magnetic field. However its power efficiency (ratio of maximum power of the emitted wave to the maximum electrical power input into the diode) is very low, of the order of approximately 1%. Furthermore, the frequencies of the emitted wave directly follow the temporal variations in the applied voltage, which leads to an electromagnetic wave being obtained of mediocre spectral quality.
To counter at least some of these drawbacks while maintaining an axial geometry, the implantation of one or more reflectors in the cylindrical wave guide 5 has been proposed.
This type of device was for example the subject of patent application WO2006/037918. An example of a device as described in that application is represented in FIGS. 3 and 4.
The reflectors are typically thin walls (that is to say of the order of the micrometer in thickness), transparent to electrons and configured to reflect totally the microwave wave 7 created by a virtual cathode. Furthermore, they are of circular cylindrical shape, that is to say disk-shaped. They are often formed of aluminized mylar.
In the example represented in FIG. 3, a first reflector 8 is positioned within the wave guide 5 at a distance D1 from the thin anode 4. This distance D1 is equal to substantially twice the distance dAk that separates the thin anode 4 from the cathode 2, such that a virtual cathode is created and positioned approximately at mid-distance from the thin anode 4 and the first reflector 8.
In this example, an additional reflector 9 is positioned in the wave guide 5 beyond the first reflector 8, such that the distance separating the two successive reflectors is equal to substantially twice the distance dAk that separates the thin anode 4 from the cathode 2, that is to say substantially the distance D1.
The reflectors may be “closed” or “open”. As illustrated by FIGS. 3 and 4, a reflector is said to be “closed” when it entirely closes a cross-section of the cylindrical wave guide 5 (this is the case, for example, for the first reflector 8), and a reflector is said to be “open” when it only obstructs a centered fraction of the cross-section of the cylindrical wave guide 5, leaving a substantially annular opening 10 between the periphery of the reflector and the inside wall of the wave guide 5 (this is the case, in the present example, for the additional reflector 9).
The reflector furthest away from the thin anode 4 is preferably open in order to promote the propagation of the microwave wave towards the exit from the cylindrical wave guide 5, the exit being the opposite end of the cylindrical wave guide 5 from that where the thin anode 4 is situated.
Conventionally, an open reflector presents a radius R greater than or equal to substantially 0.75 times the radius RG of the cylindrical wave guide 5 to reflect the maximum of the radial component of the electric field of the wave.
The first reflector 8 is operative to reflect the wave emitted by the virtual cathode, like the thin anode 4. The wave reflected by the first reflector 8 again interacts with the electrons and the virtual cathode, amplifying the microwave wave 7. A first pseudo-cavity 11, which is cylindrical, formed between the thin anode 4, the first reflector 8 and an inside wall of the wave guide 5 enables the power of the wave created by the virtual cathode to be strengthened. This strengthening of the wave contributes to improving the bunching of the electrons of the virtual cathode at the desired frequency.
By introducing a plurality of reflectors into the device (that is to say a number N), the mechanism for strengthening the microwave wave 7 and for bunching which takes place in the first pseudo-cavity 11 is duplicated in the following pseudo-cavities formed by two successive reflectors (for example the first reflector 8 and the additional reflector 9 in FIG. 3) and the cylindrical wave guide 5.
Thus the electrons which cross the reflector of rank (i) (1≦i≦N−1, where N is the total number of reflectors present) create an (i+1)th virtual cathode of which the oscillation frequency is determined by the pseudo-cavity formed by the reflectors of rank (i) and (i+1) and the inside wall of the wave guide 5. This pseudo-cavity contributes to strengthening the electromagnetic wave 7 emitted by the (i+1)th virtual cathode and the bunching of the electrons.
If the reflector (i+1) is open, the electromagnetic wave emitted by the (i+1)th virtual cathode can flow inside the wave guide 5 beyond the reflector (i+1), towards the exit from the guide, via the annular opening 10 present between the periphery of the reflector (i+1) and the inside wall of the wave guide 5.
This type of device with reflectors enables substantially improved performance to be obtained relative to the devices of the prior art without reflector.
A device, emitting in the S band at the exit from the wave guide, that is to say within a range of frequencies going from 2 GHz to 4 GHz, with a single open reflector exhibits an improvement in efficiency of the order of 4%. The addition of a second open reflector leads to an improvement of the order of 10%.
However, for such a device comprising reflectors, there is an optimum number of reflectors beyond which the power efficiency decreases. For example, a device with three open reflectors exhibits an optimum in efficiency of the order of 13%.
To still further increase the efficiency of a device of VIRCATOR type with reflectors such as described above, the French patent application filed under the Ser. No. 12/62385, and not yet published, describes a microwave wave generator device with a virtual cathode oscillator comprising a plurality of reflectors. All the reflectors are then open with the radius of each of the reflectors of the plurality being less than or equal to the radius of the preceding reflector, the radius of the last reflector being less than the radius of the first reflector. Such a device is for example represented in FIG. 5 according to an example embodiment.
The device of FIG. 5 here comprises a set of five reflectors (N=5), collectively denoted Ei and referenced here E1 to E5, which are located in the wave guide 5, transparent to electrons and configured to reflect the microwave wave created by a virtual cathode. They are for example of aluminized mylar.
All the reflectors Ei are “open” so as to facilitate the propagation of the wave emitted by the different virtual cathodes towards the exit of the wave guide 5.
The radius of the first open reflector E1 located after the thin anode 4 in the wave guide 5 is preferably greater than or equal to 0.75 RG. It thus reflects the maximum of the radial component of the electric field of the wave and thus strengthens the microwave wave emitted by the first virtual cathode that is to say the virtual cathode formed just after the thin anode 4, between the thin anode 4 and the first reflector E1.
The radius of the following reflectors Ei is progressively reduced without lower limit. The size of the radius of each reflector is possibly chosen less than 0.75 RG. The provisions for reducing the size of the radius of the open reflectors are for example the following:                The radius of the reflector of rank (i+1) is less than or equal to the radius of the reflector of rank i, that is to say of the directly preceding reflector.        The radius of the last reflector (here E5, or denoted more generally EN, whatever be N) is less than the radius of the first reflector E1.        
In the example embodiment of FIG. 5, the reflectors E1 to E4 have the same radius whereas the last reflector, E5, is of lesser radius.
A device according to the invention described in the French patent application filed under the Ser. No. 12/62385, and not yet published, enables the performance of a conventional axial VIRCATOR of the prior art to be considerably improved, and in particular that of an axial VIRCATOR with reflectors of the prior art as described in the application WO2006/037918. For example, a device with five reflectors of non-uniform radius (with the radius of each reflector less than or equal to that of the immediately preceding reflector), emitting in the S band (that is to say in a frequency range going from 2 GHz to 4 GHz), exhibits an efficiency of 21%.
The operation of the devices of VIRCATOR type of the prior art, described above, is however limited to supply generators of which the immediate Z is less than what is referred to as a “critical” impedance, denoted Z. This critical impedance Zc is defined as the ratio of the supply voltage V over the critical current Ic defined earlier, that is to say Zc=V/Ic.
FIG. 6 represents a propagation of an electron beam in the wave guide 5 in practically laminar regime when the impedance Z of the generator is greater than the critical impedance Z. This results in no virtual cathode forming. FIG. 7 represents, by way of illustration, the absence of formation of any virtual cathode oscillator in the phase space. No electron can thus be sent back towards the cathode 2 through the thin anode 4.